Logit models and logistic regressions for social networks: I. An introduction to Markov graphs andp

Spanning nearly sixty years of research, statistical network analysis has passed through (at least) two generations of researchers and models. Beginning in the late 1930's, the first generation of research dealt with the distribution of various network statistics, under a variety of null models. The second generation, beginning in the 1970's and continuing into the 1980's, concerned models, usually for probabilities of relational ties among very small subsets of actors, in which various simple substantive tendencies were parameterized. Much of this research, most of which utilized log linear models, first appeared in applied statistics publications.But recent developments in social network analysis promise to bring us into a third generation. The Markov random graphs of Frank and Strauss (1986) and especially the estimation strategy for these models developed by Strauss and Ikeda (1990; described in brief in Strauss, 1992), are very recent and promising contributions to this field. Here we describe a large class of models that can be used to investigate structure in social networks. These models include several generalizations of stochastic blockmodels, as well as models parameterizing global tendencies towards clustering and centralization, and individual differences in such tendencies. Approximate model fits are obtained using Strauss and Ikeda's (1990) estimation strategy.In this paper we describe and extend these models and demonstrate how they can be used to address a variety of substantive questions about structure in social networks.This research was supported by grants from the Australian Research Council and the National Science Foundation (#SBR93-10184). This paper was presented at the 1994 Annual Meeting of the Psychometric Society, Champaign, Illinois, June 1994. Special thanks go to Sarah Ardu for programming assistance, Laura Koehly and Garry Robins for help with this research, and to Shizuhiko Nishisato and three reviewers for their comments. INTERNETemail addresses:pattison@psych.unimelb.edu.au (PP);stanwass@uiuc.edu (SW). Affiliations: Department of Psychology, University of Melbourne (PP); Department of Psychology, Department of Statistics, and The Beckman Institute for Advanced Science and Technology, University of Illinois (SW).